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To better understand the capacity of Lagrangian Stochastic Models to simulate superdiffusive and subdiffusive tracer motion in oceanic turbulence, we examine their performance on a simple class of model velocity fields which support subdiffusive or superdiffusive regimes of tracer transport associated to power-law regions of the Lagrangian power spectrum. We focus on how well the Lagrangian Stochastic Models can replicate the subdiffusion and superdiffusion in these models, when they are provided with exact Lagrangian information. This simple test reveals fundamental limitations in the type of subdiffusion and superdiffusion which a standard hierarchy of Lagrangian Stochastic Models is able to quantitatively approximate.

Subdiffusion and Superdiffusion in Lagrangian Stochastic Models of Oceanic Transport